Manifold Structures

These classes encode the structure of a manifold.

AUTHORS:

class sage.manifolds.structure.DifferentialStructure

Bases: sage.misc.fast_methods.Singleton

The structure of a differentiable manifold over a general topological field.

chart

alias of DiffChart

homset

alias of DifferentiableManifoldHomset

scalar_field_algebra

alias of DiffScalarFieldAlgebra

subcategory(cat)

Return the subcategory of cat corresponding to the structure of self.

EXAMPLES:

sage: from sage.manifolds.structure import DifferentialStructure
sage: from sage.categories.manifolds import Manifolds
sage: DifferentialStructure().subcategory(Manifolds(RR))
Category of manifolds over Real Field with 53 bits of precision
class sage.manifolds.structure.RealDifferentialStructure

Bases: sage.misc.fast_methods.Singleton

The structure of a differentiable manifold over \(\RR\).

chart

alias of RealDiffChart

homset

alias of DifferentiableManifoldHomset

scalar_field_algebra

alias of DiffScalarFieldAlgebra

subcategory(cat)

Return the subcategory of cat corresponding to the structure of self.

EXAMPLES:

sage: from sage.manifolds.structure import DifferentialStructure
sage: from sage.categories.manifolds import Manifolds
sage: DifferentialStructure().subcategory(Manifolds(RR))
Category of manifolds over Real Field with 53 bits of precision
class sage.manifolds.structure.RealTopologicalStructure

Bases: sage.misc.fast_methods.Singleton

The structure of a topological manifold over \(\RR\).

chart

alias of RealChart

homset

alias of TopologicalManifoldHomset

scalar_field_algebra

alias of ScalarFieldAlgebra

subcategory(cat)

Return the subcategory of cat corresponding to the structure of self.

EXAMPLES:

sage: from sage.manifolds.structure import RealTopologicalStructure
sage: from sage.categories.manifolds import Manifolds
sage: RealTopologicalStructure().subcategory(Manifolds(RR))
Category of manifolds over Real Field with 53 bits of precision
class sage.manifolds.structure.TopologicalStructure

Bases: sage.misc.fast_methods.Singleton

The structure of a topological manifold over a general topological field.

chart

alias of Chart

homset

alias of TopologicalManifoldHomset

scalar_field_algebra

alias of ScalarFieldAlgebra

subcategory(cat)

Return the subcategory of cat corresponding to the structure of self.

EXAMPLES:

sage: from sage.manifolds.structure import TopologicalStructure
sage: from sage.categories.manifolds import Manifolds
sage: TopologicalStructure().subcategory(Manifolds(RR))
Category of manifolds over Real Field with 53 bits of precision